text:
Usa Florida
SECTION 1. Taxation; appropriations; state expenses; state revenue limitation.--
(a) No tax shall be levied except in pursuance of law. No state ad valorem taxes shall be levied upon real estate or tangible personal property. All other forms of taxation shall be preempted to the state except as provided by general law.
(b) Motor vehicles, boats, airplanes, trailers, trailer coaches and mobile homes, as defined by law, shall be subject to a license tax for their operation in the amounts and for the purposes prescribed by law, but shall not be subject to ad valorem taxes.
(c) No money shall be drawn from the treasury except in pursuance of appropriation made by law.
(d) Provision shall be made by law for raising sufficient revenue to defray the expenses of the state for each fiscal period.
(e) Except as provided herein, state revenues collected for any fiscal year shall be limited to state revenues allowed under this subsection for the prior fiscal year plus an adjustment for growth. As used in this subsection, "growth" means an amount equal to the average annual rate of growth in Florida personal income over the most recent twenty quarters times the state revenues allowed under this subsection for the prior fiscal year. For the 1995-1996 fiscal year, the state revenues allowed under this subsection for the prior fiscal year shall equal the state revenues collected for the 1994-1995 fiscal year. Florida personal income shall be determined by the legislature, from information available from the United States Department of Commerce or its successor on the first day of February prior to the beginning of the fiscal year. State revenues collected for any fiscal year in excess of this limitation shall be transferred to the budget stabilization fund until the fund reaches the maximum balance specified in Section 19(g) of Article III, and thereafter shall be refunded to taxpayers as provided by general law. State revenues allowed under this subsection for any fiscal year may be increased by a two-thirds vote of the membership of each house of the legislature in a separate bill that contains no other subject and that sets forth the dollar amount by which the state revenues allowed will be increased. The vote may not be taken less than seventy-two hours after the third reading of the bill. For purposes of this subsection, "state revenues" means taxes, fees, licenses, and charges for services imposed by the legislature on individuals, businesses, or agencies outside state government. However, "state revenues" does not include: revenues that are necessary to meet the requirements set forth in documents authorizing the issuance of bonds by the state; revenues that are used to provide matching funds for the federal Medicaid program with the exception of the revenues used to support the Public Medical Assistance Trust Fund or its successor program and with the exception of state matching funds used to fund elective expansions made after July 1, 1994; proceeds from the state lottery returned as prizes; receipts of the Florida Hurricane Catastrophe Fund; balances carried forward from prior fiscal years; taxes, licenses, fees, and charges for services imposed by local, regional, or school district governing bodies; or revenue from taxes, licenses, fees, and charges for services required to be imposed by any amendment or revision to this constitution after July 1, 1994. An adjustment to the revenue limitation shall be made by general law to reflect the fiscal impact of transfers of responsibility for the funding of governmental functions between the state and other levels of government. The legislature shall, by general law, prescribe procedures necessary to administer this subsection.
History.--Am. H.J.R. 2053, 1994; adopted 1994.
SECTION 2. Taxes; rate.--All ad valorem taxation shall be at a uniform rate within each taxing unit, except the taxes on intangible personal property may be at different rates but shall never exceed two mills on the dollar of assessed value; provided, as to any obligations secured by mortgage, deed of trust, or other lien on real estate wherever located, an intangible tax of not more than two mills on the dollar may be levied by law to be in lieu of all other intangible assessments on such obligations.
SECTION 3. Taxes; exemptions.--
(a) All property owned by a municipality and used exclusively by it for municipal or public purposes shall be exempt from taxation. A municipality, owning property outside the municipality, may be required by general law to make payment to the taxing unit in which the property is located. Such portions of property as are used predominantly for educational, literary, scientific, religious or charitable purposes may be exempted by general law from taxation.
(b) There shall be exempt from taxation, cumulatively, to every head of a family residing in this state, household goods and personal effects to the value fixed by general law, not less than one thousand dollars, and to every widow or widower or person who is blind or totally and permanently disabled, property to the value fixed by general law not less than five hundred dollars.
(c) Any county or municipality may, for the purpose of its respective tax levy and subject to the provisions of this subsection and general law, grant community and economic development ad valorem tax exemptions to new businesses and expansions of existing businesses, as defined by general law. Such an exemption may be granted only by ordinance of the county or municipality, and only after the electors of the county or municipality voting on such question in a referendum authorize the county or municipality to adopt such ordinances. An exemption so granted shall apply to improvements to real property made by or for the use of a new business and improvements to real property related to the expansion of an existing business and shall also apply to tangible personal property of such new business and tangible personal property related to the expansion of an existing business. The amount or limits of the amount of such exemption shall be specified by general law. The period of time for which such exemption may be granted to a new business or expansion of an existing business shall be determined by general law. The authority to grant such exemption shall expire ten years from the date of approval by the electors of the county or municipality, and may be renewable by referendum as provided by general law.
(d) Any county or municipality may, for the purpose of its respective tax levy and subject to the provisions of this subsection and general law, grant historic preservation ad valorem tax exemptions to owners of historic properties. This exemption may be granted only by ordinance of the county or municipality. The amount or limits of the amount of this exemption and the requirements for eligible properties must be specified by general law. The period of time for which this exemption may be granted to a property owner shall be determined by general law.
(e) By general law and subject to conditions specified therein, twenty-five thousand dollars of the assessed value of property subject to tangible personal property tax shall be exempt from ad valorem taxation.
1(f) There shall be granted an ad valorem tax exemption for real property dedicated in perpetuity for conservation purposes, including real property encumbered by perpetual conservation easements or by other perpetual conservation protections, as defined by general law.
History.--Am. S.J.R.'s 9-E, 15-E, 1980; adopted 1980; Am. C.S. for S.J.R.'s 318, 356, 1988; adopted 1988; Am. S.J.R. 152, 1992; adopted 1992; Am. H.J.R. 969, 1997; adopted 1998; Am. C.S. for S.J.R. 2-D, 2007; adopted 2008; Ams. proposed by Taxation and Budget Reform Commission, Revision Nos. 3 and 4, 2008, filed with the Secretary of State April 28, 2008; adopted 2008.
1Note.--This subsection, originally designated (g) by Revision No. 4 of the Taxation and Budget Reform Commission, 2008, was redesignated (f) by the editors to conform to the redesignation of subsections by Revision No. 3 of the Taxation and Budget Reform Commission, 2008.
SECTION 4. Taxation; assessments.--By general law regulations shall be prescribed which shall secure a just valuation of all property for ad valorem taxation, provided:
(a) Agricultural land, land producing high water recharge to Florida's aquifers, or land used exclusively for noncommercial recreational purposes may be classified by general law and assessed solely on the basis of character or use.
(b) As provided by general law and subject to conditions, limitations, and reasonable definitions specified therein, land used for conservation purposes shall be classified by general law and assessed solely on the basis of character or use.
(c) Pursuant to general law tangible personal property held for sale as stock in trade and livestock may be valued for taxation at a specified percentage of its value, may be classified for tax purposes, or may be exempted from taxation.
(d) All persons entitled to a homestead exemption under Section 6 of this Article shall have their homestead assessed at just value as of January 1 of the year following the effective date of this amendment. This assessment shall change only as provided in this subsection.
(1) Assessments subject to this subsection shall be changed annually on January 1st of each year; but those changes in assessments shall not exceed the lower of the following:
a. Three percent (3%) of the assessment for the prior year.
b. The percent change in the Consumer Price Index for all urban consumers, U.S. City Average, all items 1967=100, or successor reports for the preceding calendar year as initially reported by the United States Department of Labor, Bureau of Labor Statistics.
(2) No assessment shall exceed just value.
(3) After any change of ownership, as provided by general law, homestead property shall be assessed at just value as of January 1 of the following year, unless the provisions of paragraph (8) apply. Thereafter, the homestead shall be assessed as provided in this subsection.
(4) New homestead property shall be assessed at just value as of January 1st of the year following the establishment of the homestead, unless the provisions of paragraph (8) apply. That assessment shall only change as provided in this subsection.
(5) Changes, additions, reductions, or improvements to homestead property shall be assessed as provided for by general law; provided, however, after the adjustment for any change, addition, reduction, or improvement, the property shall be assessed as provided in this subsection.
(6) In the event of a termination of homestead status, the property shall be assessed as provided by general law.
(7) The provisions of this amendment are severable. If any of the provisions of this amendment shall be held unconstitutional by any court of competent jurisdiction, the decision of such court shall not affect or impair any remaining provisions of this amendment.
(8)a. A person who establishes a new homestead as of January 1, 2009, or January 1 of any subsequent year and who has received a homestead exemption pursuant to Section 6 of this Article as of January 1 of either of the two years immediately preceding the establishment of the new homestead is entitled to have the new homestead assessed at less than just value. If this revision is approved in January of 2008, a person who establishes a new homestead as of January 1, 2008, is entitled to have the new homestead assessed at less than just value only if that person received a homestead exemption on January 1, 2007. The assessed value of the newly established homestead shall be determined as follows:
1. If the just value of the new homestead is greater than or equal to the just value of the prior homestead as of January 1 of the year in which the prior homestead was abandoned, the assessed value of the new homestead shall be the just value of the new homestead minus an amount equal to the lesser of $500,000 or the difference between the just value and the assessed value of the prior homestead as of January 1 of the year in which the prior homestead was abandoned. Thereafter, the homestead shall be assessed as provided in this subsection.
2. If the just value of the new homestead is less than the just value of the prior homestead as of January 1 of the year in which the prior homestead was abandoned, the assessed value of the new homestead shall be equal to the just value of the new homestead divided by the just value of the prior homestead and multiplied by the assessed value of the prior homestead. However, if the difference between the just value of the new homestead and the assessed value of the new homestead calculated pursuant to this sub-subparagraph is greater than $500,000, the assessed value of the new homestead shall be increased so that the difference between the just value and the assessed value equals $500,000. Thereafter, the homestead shall be assessed as provided in this subsection.
b. By general law and subject to conditions specified therein, the Legislature shall provide for application of this paragraph to property owned by more than one person.
(e) The legislature may, by general law, for assessment purposes and subject to the provisions of this subsection, allow counties and municipalities to authorize by ordinance that historic property may be assessed solely on the basis of character or use. Such character or use assessment shall apply only to the jurisdiction adopting the ordinance. The requirements for eligible properties must be specified by general law.
(f) A county may, in the manner prescribed by general law, provide for a reduction in the assessed value of homestead property to the extent of any increase in the assessed value of that property which results from the construction or reconstruction of the property for the purpose of providing living quarters for one or more natural or adoptive grandparents or parents of the owner of the property or of the owner's spouse if at least one of the grandparents or parents for whom the living quarters are provided is 62 years of age or older. Such a reduction may not exceed the lesser of the following:
(1) The increase in assessed value resulting from construction or reconstruction of the property.
(2) Twenty percent of the total assessed value of the property as improved.
(g) For all levies other than school district levies, assessments of residential real property, as defined by general law, which contains nine units or fewer and which is not subject to the assessment limitations set forth in subsections (a) through (d) shall change only as provided in this subsection.
(1) Assessments subject to this subsection shall be changed annually on the date of assessment provided by law; but those changes in assessments shall not exceed ten percent (10%) of the assessment for the prior year.
(3) After a change of ownership or control, as defined by general law, including any change of ownership of a legal entity that owns the property, such property shall be assessed at just value as of the next assessment date. Thereafter, such property shall be assessed as provided in this subsection.
(4) Changes, additions, reductions, or improvements to such property shall be assessed as provided for by general law; however, after the adjustment for any change, addition, reduction, or improvement, the property shall be assessed as provided in this subsection.
(h) For all levies other than school district levies, assessments of real property that is not subject to the assessment limitations set forth in subsections (a) through (d) and (g) shall change only as provided in this subsection.
(3) The legislature must provide that such property shall be assessed at just value as of the next assessment date after a qualifying improvement, as defined by general law, is made to such property. Thereafter, such property shall be assessed as provided in this subsection.
(4) The legislature may provide that such property shall be assessed at just value as of the next assessment date after a change of ownership or control, as defined by general law, including any change of ownership of the legal entity that owns the property. Thereafter, such property shall be assessed as provided in this subsection.
1(i) The legislature, by general law and subject to conditions specified therein, may prohibit the consideration of the following in the determination of the assessed value of real property used for residential purposes:
(1) Any change or improvement made for the purpose of improving the property's resistance to wind damage.
(2) The installation of a renewable energy source device.
2(j)(1) The assessment of the following working waterfront properties shall be based upon the current use of the property:
a. Land used predominantly for commercial fishing purposes.
b. Land that is accessible to the public and used for vessel launches into waters that are navigable.
c. Marinas and drystacks that are open to the public.
d. Water-dependent marine manufacturing facilities, commercial fishing facilities, and marine vessel construction and repair facilities and their support activities.
(2) The assessment benefit provided by this subsection is subject to conditions and limitations and reasonable definitions as specified by the legislature by general law.
History.--Am. S.J.R. 12-E, 1980; adopted 1980; Am. H.J.R. 214, 1987; adopted 1988; Am. by Initiative Petition filed with the Secretary of State August 3, 1992; adopted 1992; Am. H.J.R. 969, 1997; adopted 1998; Am. proposed by Constitution Revision Commission, Revision No. 13, 1998, filed with the Secretary of State May 5, 1998; adopted 1998; Am. C.S. for H.J.R. 317, 2002; adopted 2002; Am. C.S. for S.J.R. 2-D, 2007; adopted 2008; Ams. Proposed by Taxation and Budget Reform Commission, Revision Nos. 3, 4, and 6, 2008, filed with the Secretary of State April 28, 2008; adopted 2008.
1Note.--This subsection, originally designated (h) by Revision No. 3 of the Taxation and Budget Reform Commission, 2008, was redesignated (i) by the editors to conform to the redesignation of subsections by Revision No. 4 of the Taxation and Budget Reform Commission, 2008.
2Note.--This subsection, originally designated (h) by Revision No. 6 of the Taxation and Budget Reform Commission, 2008, was redesignated (j) by the editors to conform to the redesignation of subsections by Revision No. 4 of the Taxation and Budget Reform Commission, 2008, and the creation of a new (h) by Revision No. 3 of the Taxation and Budget Reform Commission, 2008.
SECTION 5. Estate, inheritance and income taxes.--
(a) NATURAL PERSONS. No tax upon estates or inheritances or upon the income of natural persons who are residents or citizens of the state shall be levied by the state, or under its authority, in excess of the aggregate of amounts which may be allowed to be credited upon or deducted from any similar tax levied by the United States or any state.
(b) OTHERS. No tax upon the income of residents and citizens other than natural persons shall be levied by the state, or under its authority, in excess of 5% of net income, as defined by law, or at such greater rate as is authorized by a three-fifths (3/5) vote of the membership of each house of the legislature or as will provide for the state the maximum amount which may be allowed to be credited against income taxes levied by the United States and other states. There shall be exempt from taxation not less than five thousand dollars ($5,000) of the excess of net income subject to tax over the maximum amount allowed to be credited against income taxes levied by the United States and other states.
(c) EFFECTIVE DATE. This section shall become effective immediately upon approval by the electors of Florida.
History.--Am. H.J.R. 7-B, 1971; adopted 1971.
SECTION 6. Homestead exemptions.--
(a) Every person who has the legal or equitable title to real estate and maintains thereon the permanent residence of the owner, or another legally or naturally dependent upon the owner, shall be exempt from taxation thereon, except assessments for special benefits, up to the assessed valuation of twenty-five thousand dollars and, for all levies other than school district levies, on the assessed valuation greater than fifty thousand dollars and up to seventy-five thousand dollars, upon establishment of right thereto in the manner prescribed by law. The real estate may be held by legal or equitable title, by the entireties, jointly, in common, as a condominium, or indirectly by stock ownership or membership representing the owner's or member's proprietary interest in a corporation owning a fee or a leasehold initially in excess of ninety-eight years. The exemption shall not apply with respect to any assessment roll until such roll is first determined to be in compliance with the provisions of section 4 by a state agency designated by general law. This exemption is repealed on the effective date of any amendment to this Article which provides for the assessment of homestead property at less than just value.
(b) Not more than one exemption shall be allowed any individual or family unit or with respect to any residential unit. No exemption shall exceed the value of the real estate assessable to the owner or, in case of ownership through stock or membership in a corporation, the value of the proportion which the interest in the corporation bears to the assessed value of the property.
(c) By general law and subject to conditions specified therein, the Legislature may provide to renters, who are permanent residents, ad valorem tax relief on all ad valorem tax levies. Such ad valorem tax relief shall be in the form and amount established by general law.
(d) The legislature may, by general law, allow counties or municipalities, for the purpose of their respective tax levies and subject to the provisions of general law, to grant an additional homestead tax exemption not exceeding fifty thousand dollars to any person who has the legal or equitable title to real estate and maintains thereon the permanent residence of the owner and who has attained age sixty-five and whose household income, as defined by general law, does not exceed twenty thousand dollars. The general law must allow counties and municipalities to grant this additional exemption, within the limits prescribed in this subsection, by ordinance adopted in the manner prescribed by general law, and must provide for the periodic adjustment of the income limitation prescribed in this subsection for changes in the cost of living.
(e) Each veteran who is age 65 or older who is partially or totally permanently disabled shall receive a discount from the amount of the ad valorem tax otherwise owed on homestead property the veteran owns and resides in if the disability was combat related, the veteran was a resident of this state at the time of entering the military service of the United States, and the veteran was honorably discharged upon separation from military service. The discount shall be in a percentage equal to the percentage of the veteran's permanent, service-connected disability as determined by the United States Department of Veterans Affairs. To qualify for the discount granted by this subsection, an applicant must submit to the county property appraiser, by March 1, proof of residency at the time of entering military service, an official letter from the United States Department of Veterans Affairs stating the percentage of the veteran's service-connected disability and such evidence that reasonably identifies the disability as combat related, and a copy of the veteran's honorable discharge. If the property appraiser denies the request for a discount, the appraiser must notify the applicant in writing of the reasons for the denial, and the veteran may reapply. The Legislature may, by general law, waive the annual application requirement in subsequent years. This subsection shall take effect December 7, 2006, is self-executing, and does not require implementing legislation.
History.--Am. S.J.R. 1-B, 1979; adopted 1980; Am. S.J.R. 4-E, 1980; adopted 1980; Am. H.J.R. 3151, 1998; adopted 1998; Am. proposed by Constitution Revision Commission, Revision No. 13, 1998, filed with the Secretary of State May 5, 1998; adopted 1998; Am. H.J.R. 353, 2006; adopted 2006; Am. H.J.R. 631, 2006; adopted 2006; Am. C.S. for S.J.R. 2-D, 2007; adopted 2008.
SECTION 7. Allocation of par-mutual taxes.--Taxes upon the operation of par-mutual pools may be preempted to the state or allocated in whole or in part to the counties. When allocated to the counties, the distribution shall be in equal amounts to the several counties.
SECTION 8. Aid to local governments.--State funds may be appropriated to the several counties, school districts, municipalities or special districts upon such conditions as may be provided by general law. These conditions may include the use of relative ad valorem assessment levels determined by a state agency designated by general law.
History.--Am. S.J.R. 4-E, 1980; adopted 1980.
SECTION 9. Local taxes.--
(a) Counties, school districts, and municipalities shall, and special districts may, be authorized by law to levy ad valorem taxes and may be authorized by general law to levy other taxes, for their respective purposes, except ad valorem taxes on intangible personal property and taxes prohibited by this constitution.
(b) Ad valorem taxes, exclusive of taxes levied for the payment of bonds and taxes levied for periods not longer than two years when authorized by vote of the electors who are the owners of freeholds therein not wholly exempt from taxation, shall not be levied in excess of the following millages upon the assessed value of real estate and tangible personal property: for all county purposes, ten mills; for all municipal purposes, ten mills; for all school purposes, ten mills; for water management purposes for the northwest portion of the state lying west of the line between ranges two and three east, 0.05 mill; for water management purposes for the remaining portions of the state, 1.0 mill; and for all other special districts a millage authorized by law approved by vote of the electors who are owners of freeholds therein not wholly exempt from taxation. A county furnishing municipal services may, to the extent authorized by law, levy additional taxes within the limits fixed for municipal purposes.
History.--Am. S.J.R. 1061, 1975; adopted 1976.
SECTION 10. Pledging credit.--Neither the state nor any county, school district, municipality, special district, or agency of any of them, shall become a joint owner with, or stockholder of, or give, lend or use its taxing power or credit to aid any corporation, association, partnership or person; but this shall not prohibit laws authorizing:
(a) the investment of public trust funds;
(b) the investment of other public funds in obligations of, or insured by, the United States or any of its instrumentalities;
(c) the issuance and sale by any county, municipality, special district or other local governmental body of (1) revenue bonds to finance or refinance the cost of capital projects for airports or port facilities, or (2) revenue bonds to finance or refinance the cost of capital projects for industrial or manufacturing plants to the extent that the interest thereon is exempt from income taxes under the then existing laws of the United States, when, in either case, the revenue bonds are payable solely from revenue derived from the sale, operation or leasing of the projects. If any project so financed, or any part thereof, is occupied or operated by any private corporation, association, partnership or person pursuant to contract or lease with the issuing body, the property interest created by such contract or lease shall be subject to taxation to the same extent as other privately owned property.
(d) a municipality, county, special district, or agency of any of them, being a joint owner of, giving, or lending or using its taxing power or credit for the joint ownership, construction and operation of electrical energy generating or transmission facilities with any corporation, association, partnership or person.
SECTION 11. State bonds; revenue bonds.--
(a) State bonds pledging the full faith and credit of the state may be issued only to finance or refinance the cost of state fixed capital outlay projects authorized by law, and purposes incidental thereto, upon approval by a vote of the electors; provided state bonds issued pursuant to this subsection may be refunded without a vote of the electors at a lower net average interest cost rate. The total outstanding principal of state bonds issued pursuant to this subsection shall never exceed fifty percent of the total tax revenues of the state for the two preceding fiscal years, excluding any tax revenues held in trust under the provisions of this constitution.
(b) Moneys sufficient to pay debt service on state bonds as the same becomes due shall be appropriated by law.
(c) Any state bonds pledging the full faith and credit of the state issued under this section or any other section of this constitution may be combined for the purposes of sale.
(d) Revenue bonds may be issued by the state or its agencies without a vote of the electors to finance or refinance the cost of state fixed capital outlay projects authorized by law, and purposes incidental thereto, and shall be payable solely from funds derived directly from sources other than state tax revenues.
(e) Bonds pledging all or part of a dedicated state tax revenue may be issued by the state in the manner provided by general law to finance or refinance the acquisition and improvement of land, water areas, and related property interests and resources for the purposes of conservation, outdoor recreation, water resource development, restoration of natural systems, and historic preservation.
(f) Each project, building, or facility to be financed or refinanced with revenue bonds issued under this section shall first be approved by the Legislature by an act relating to appropriations or by general law.
History.--Am. C.S. for C.S. for S.J.R. 612, 1984; adopted 1984; Am. proposed by Constitution Revision Commission, Revision No. 5, 1998, filed with the Secretary of State May 5, 1998; adopted 1998.
SECTION 12. Local bonds.--Counties, school districts, municipalities, special districts and local governmental bodies with taxing powers may issue bonds, certificates of indebtedness or any form of tax anticipation certificates, payable from ad valorem taxation and maturing more than twelve months after issuance only:
(a) to finance or refinance capital projects authorized by law and only when approved by vote of the electors who are owners of freeholds therein not wholly exempt from taxation; or
(b) to refund outstanding bonds and interest and redemption premium thereon at a lower net average interest cost rate.
SECTION 13. Relief from illegal taxes.--Until payment of all taxes which have been legally assessed upon the property of the same owner, no court shall grant relief from the payment of any tax that may be illegal or illegally assessed.
SECTION 14. Bonds for pollution control and abatement and other water facilities.--
(a) When authorized by law, state bonds pledging the full faith and credit of the state may be issued without an election to finance the construction of air and water pollution control and abatement and solid waste disposal facilities and other water facilities authorized by general law (herein referred to as "facilities") to be operated by any municipality, county, district or authority, or any agency thereof (herein referred to as "local governmental agencies"), or by any agency of the State of Florida. Such bonds shall be secured by a pledge of and shall be payable primarily from all or any part of revenues to be derived from operation of such facilities, special assessments, rentals to be received under lease-purchase agreements herein provided for, any other revenues that may be legally available for such purpose, including revenues from other facilities, or any combination thereof (herein collectively referred to as "pledged revenues"), and shall be additionally secured by the full faith and credit of the State of Florida.
(b) No such bonds shall be issued unless a state fiscal agency, created by law, has made a determination that in no state fiscal year will the debt service requirements of the bonds proposed to be issued and all other bonds secured by the pledged revenues exceed seventy-five per cent of the pledged revenues.
(c) The state may lease any of such facilities to any local governmental agency, under lease-purchase agreements for such periods and under such other terms and conditions as may be mutually agreed upon. The local governmental agencies may pledge the revenues derived from such leased facilities or any other available funds for the payment of rentals thereunder; and, in addition, the full faith and credit and taxing power of such local governmental agencies may be pledged for the payment of such rentals without any election of freeholder electors or qualified electors.
(d) The state may also issue such bonds for the purpose of loaning money to local governmental agencies, for the construction of such facilities to be owned or operated by any of such local governmental agencies. Such loans shall bear interest at not more than one-half of one per cent per annum greater than the last preceding issue of state bonds pursuant to this section, shall be secured by the pledged revenues, and may be additionally secured by the full faith and credit of the local governmental agencies.
(e) The total outstanding principal of state bonds issued pursuant to this section 14 shall never exceed fifty per cent of the total tax revenues of the state for the two preceding fiscal years.
History.--C.S. for H.J.R.'s 3853, 4040, 1970; adopted 1970; Am. H.J.R. 1471, 1980; adopted 1980.
SECTION 15. Revenue bonds for scholarship loans.--
(a) When authorized by law, revenue bonds may be issued to establish a fund to make loans to students determined eligible as prescribed by law and who have been admitted to attend any public or private institutions of higher learning, junior colleges, health related training institutions, or vocational training centers, which are recognized or accredited under terms and conditions prescribed by law. Revenue bonds issued pursuant to this section shall be secured by a pledge of and shall be payable primarily from payments of interest, principal, and handling charges to such fund from the recipients of the loans and, if authorized by law, may be additionally secured by student fees and by any other moneys in such fund. There shall be established from the proceeds of each issue of revenue bonds a reserve account in an amount equal to and sufficient to pay the greatest amount of principal, interest, and handling charges to become due on such issue in any ensuing state fiscal year.
(b) Interest moneys in the fund established pursuant to this section, not required in any fiscal year for payment of debt service on then outstanding revenue bonds or for maintenance of the reserve account, may be used for educational loans to students determined to be eligible therefor in the manner provided by law, or for such other related purposes as may be provided by law.
History.--Added, H.J.R. 46-D, 1971; adopted 1972.
SECTION 16. Bonds for housing and related facilities.--
(a) When authorized by law, revenue bonds may be issued without an election to finance or refinance housing and related facilities in Florida, herein referred to as "facilities."
(b) The bonds shall be secured by a pledge of and shall be payable primarily from all or any part of revenues to be derived from the financing, operation or sale of such facilities, mortgage or loan payments, and any other revenues or assets that may be legally available for such purposes derived from sources other than ad valorem taxation, including revenues from other facilities, or any combination thereof, herein collectively referred to as "pledged revenues," provided that in no event shall the full faith and credit of the state be pledged to secure such revenue bonds.
(c) No bonds shall be issued unless a state fiscal agency, created by law, has made a determination that in no state fiscal year will the debt service requirements of the bonds proposed to be issued and all other bonds secured by the same pledged revenues exceed the pledged revenues available for payment of such debt service requirements, as defined by law.
History.--Added, S.J.R. 6-E, 1980; adopted 1980.
cf.--s. 18, Art. XII Schedule.
SECTION 17. Bonds for acquiring transportation right-of-way or for constructing bridges.--
(a) When authorized by law, state bonds pledging the full faith and credit of the state may be issued, without a vote of the electors, to finance or refinance the cost of acquiring real property or the rights to real property for state roads as defined by law, or to finance or refinance the cost of state bridge construction, and purposes incidental to such property acquisition or state bridge construction.
(b) Bonds issued under this section shall be secured by a pledge of and shall be payable primarily from motor fuel or special fuel taxes, except those defined in Section 9(c) of Article XII, as provided by law, and shall additionally be secured by the full faith and credit of the state.
(c) No bonds shall be issued under this section unless a state fiscal agency, created by law, has made a determination that in no state fiscal year will the debt service requirements of the bonds proposed to be issued and all other bonds secured by the same pledged revenues exceed ninety percent of the pledged revenues available for payment of such debt service requirements, as defined by law. For the purposes of this subsection, the term "pledged revenues" means all revenues pledged to the payment of debt service, excluding any pledge of the full faith and credit of the state.
History.--Added, C.S. for C.S. for S.J.R. 391, 1988; adopted 1988.
SECTION 18. Laws requiring counties or municipalities to spend funds or limiting their ability to raise revenue or receive state tax revenue.--
(a) No county or municipality shall be bound by any general law requiring such county or municipality to spend funds or to take an action requiring the expenditure of funds unless the legislature has determined that such law fulfills an important state interest and unless: funds have been appropriated that have been estimated at the time of enactment to be sufficient to fund such expenditure; the legislature authorizes or has authorized a county or municipality to enact a funding source not available for such county or municipality on February 1, 1989, that can be used to generate the amount of funds estimated to be sufficient to fund such expenditure by a simple majority vote of the governing body of such county or municipality; the law requiring such expenditure is approved by two-thirds of the membership in each house of the legislature; the expenditure is required to comply with a law that applies to all persons similarly situated, including the state and local governments; or the law is either required to comply with a federal requirement or required for eligibility for a federal entitlement, which federal requirement specifically contemplates actions by counties or municipalities for compliance.
(b) Except upon approval of each house of the legislature by two-thirds of the membership, the legislature may not enact, amend, or repeal any general law if the anticipated effect of doing so would be to reduce the authority that municipalities or counties have to raise revenues in the aggregate, as such authority exists on February 1, 1989.
(c) Except upon approval of each house of the legislature by two-thirds of the membership, the legislature may not enact, amend, or repeal any general law if the anticipated effect of doing so would be to reduce the percentage of a state tax shared with counties and municipalities as an aggregate on February 1, 1989. The provisions of this subsection shall not apply to enhancements enacted after February 1, 1989, to state tax sources, or during a fiscal emergency declared in a written joint proclamation issued by the president of the senate and the speaker of the house of representatives, or where the legislature provides additional state-shared revenues which are anticipated to be sufficient to replace the anticipated aggregate loss of state-shared revenues resulting from the reduction of the percentage of the state tax shared with counties and municipalities, which source of replacement revenues shall be subject to the same requirements for repeal or modification as provided herein for a state-shared tax source existing on February 1, 1989.
(d) Laws adopted to require funding of pension benefits existing on the effective date of this section, criminal laws, election laws, the general appropriations act, special appropriations acts, laws reauthorizing but not expanding then-existing statutory authority, laws having insignificant fiscal impact, and laws creating, modifying, or repealing noncriminal infractions, are exempt from the requirements of this section.
(e) The legislature may enact laws to assist in the implementation and enforcement of this section.
History.--Added, C.S. for C.S. for C.S. for C.S. for H.J.R.'s 139, 40, 1989; adopted 1990.
Constitution : Usa-florida
Suffrage and Elections


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text:
1950-ті роки в театрі

Події

Прем'єри

 21 жовтня — «З іскри» Шалва Дадіані (реж. Василь Ванін, Камерний театр Таїрова, реорганізований у Московський драматичний театр ім. Олександра Пушкіна)

Персоналії

Народилися

 30 червня —
  Павло Швець (с. Волошкове Чернівецької області) — артист балету Чернівецького музично-драматичного театру ім. Ольги Кобилянської, фотожурналіст, художник-оформлювач.

 13 червня —
  Микола Прядченко (с. Вінницькі Стави Васильківського району Київської області) — український балетмейстер і педагог. Народний артист УРСР (1982).
 29 жовтня —
  Ярослав Гаврилюк (м. Львів) — український актор театру і кіно, Народний артист України.

 27 грудня —
  Олексій Рубинський (м. Дніпропетровськ) — український актор, режисер, драматург, театральний діяч, художник-графік. Народний артист України (2005).

 13 січня —
  Володимир Смотритель (м. Городище Черкаської області) — український театральний актор, керівник та актор монотеатру «Кут» (м. Хмельницький), народний артист України (2016).
 7 лютого —
  Ігор Славинський (м. Фастів) — провідний актор та режисер-постановник Київського академічного драматичного театру на Подолі, з 2008 — режисер-постановник Київського академічного драматичного театру на Подолі, з 2013 року — керівник київського театру «Актор», Народний артист України (2018).
 12 лютого —
  Микола Завгородній (с. Велике Краснодарський край) — український театральний актор, Народний артист України (2014), соліст-вокаліст Одеського академічного театру музичної комедії ім. М. Водяного.
 21 липня —
  Сергій Романюк (м. Кривий Ріг) — український актор театру і кіно, Народний артист України (1998).

 28 листопада —
  Сергій Проскурня (м. Львів) — український театральний режисер, продюсер, лауреат премій Національної спілки театральних діячів України «Експеримент» (2001) та імені Сергія Данченка (2017).

 4 травня —
  Микола Данько (с. В'юнище Переяслав-Хмельницького району Київської області) — український театральний художник. Головний художник Київського державного академічного театру ляльок.
 21 липня —
  Наталія Кудря (с. Попільня Попільнянського району Житомирської області) — українська акторка, народна артистка України (2006)

Померли

 25 вересня —
  Олександр Таїров (65) — радянський театральний актор і режисер. Засновник та художній керівник Камерного театру (1914 — 1949). Народний артист РРФСР (1935).

 1 листопада —
  Євген Золотаренко (65) — український радянський театральний актор, народний артист УРСР (1954)

Примітки

Посилання

1950-ті
Роки у театрі

redpajama_set_name: RedPajamaWikipedia


text:
JSW Steel, ArcelorMittal, Tata Steel vie for Bhushan Steel
By: PTI |
New Delhi | Published: February 4, 2018 3:17:34 PM
Top steel makers JSW Steel and Tata Steel from India, and Luxembourg-based ArcelorMittal are learnt to have submitted bids for the debt-ridden Bhushan Steel which is undergoing insolvency proceedings.
The last date to submit bids for Bhushan Steel, the maker of auto grade steel in India, was February 3.
Top steel makers JSW Steel and Tata Steel from India, and Luxembourg-based ArcelorMittal are learnt to have submitted bids for the debt-ridden Bhushan Steel which is undergoing insolvency proceedings. The last date to submit bids for Bhushan Steel, the maker of auto grade steel in India, was February 3. According to sources, JSW Steel along with Piramal Enterprises has submitted the resolution plan. Besides, Tata Steel and NRI billionaire Lakshmi Niwas Mittal-led ArcelorMittal have also bid for Bhushan Steel, sources said. An email query to sent to Tata Steel, ArcelorMittal and JSW Steel remained unanswered. The highest bidder would to announced on Tuesday.
Bhushan Steel, one of the 12 non-performing accounts referred by the Reserve Bank of India for National Company Law Tribunal (NCLT) proceedings, owes Rs 44,478 crore to lenders. According to the information on Bhushan Steel's website, the company is the third largest secondary steel producer in the country with an existing steel production capacity of 5.6 million tonne per annum.

redpajama_set_name: RedPajamaCommonCrawl


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text:
\section{Introduction}

First-order and second-order stock market models are relatively simple stochastic models that manifest some of the stability properties of actual stock market behavior. These models are descriptive as opposed to normative, and are constructed using data analysis based on actual stock markets. First-order models are stock-market models where the parameters for return and volatility  are based on the ranks of the stocks. These models were introduced in \citeN{F:2002} and developed in \citeN{BFK:2005}, and reflect the actual rank-based growth rates and variances of the stocks in the market. First-order models are asymptotically stable, and accurately reproduce the long-term characteristics of the market's capital distribution. However, these models are ergodic in the sense that each stock asymptotically spends equal  average time at each rank, and this ergodicity property does not seem to be present in actual markets. This lack of verisimilitude is the motivation to consider the next level of complexity: second-order models.

Second-order models are a form of hybrid Atlas models, where the return and volatility parameters are based on the rank and the name (or index) of the stocks (see \shortciteN{IPBKF:2011}). While these models retain many of the characteristics of first-order models, the above ergodicity property is no longer present, and this produces a more realistic representation of actual stock market behavior. In second-order models, larger stocks tend to remain asymptotically among larger stocks, and smaller stocks tend to remain among smaller stocks. This behavior is closer to that of actual stock markets, so second-order models provide a more accurate descriptive representation of stock market behavior.

Estimation of the parameters for first-order models is fairly straightforward, and  can be accomplished without great ado. Second-order parameter estimation is somewhat more complicated. Here we shall focus on the growth-rate parameters, and find it necessary to rely on implicit methods to determine values for these parameters. Our purpose here is to develop techniques for estimating second-order growth-rate parameters, not to carry out an exhaustive examination of these parameters for an entire stock market. First, let us establish some formal definitions.

A \emph{market}  is a family of \emph{stocks} $X=(X_1,\ldots,X_n)$ whose capitalizations are modeled by continuous, positive semimartingales that satisfy
\begin{equation}\label{00}
d\log X_i(t) = G_i(t)\,dt + \sum_{\nu=1}^d S_{i\nu}(t)\,dB_\nu(t),
\end{equation}
for $t\in{\mathbb R}$, where $n\le d$, $B=(B_1,\ldots,B_d)$ is an ${\mathbb R}^d$-valued Brownian motion defined on ${\mathbb R}$, and the $G_i$ and $S_{i\nu}$ are progressively measurable with respect to the Brownian filtration, with $G_i$ locally integrable and $S_{i\nu}$ locally square-integrable. The reason we define these processes on ${\mathbb R}$ is that in practice we are confronted with time series over a given block of time, and the analysis of these series can be performed in both forward and reversed  time. Hence, we see a sample in time of the processes $X_1,\ldots,X_n$ and  draw our conclusions from this sample.

We shall assume that  for any $i\ne j$, the intersection sets $\{t:X_i(t)=X_j(t)\}$  have Lebesgue measure zero, almost surely, and we shall also assume that there are no {\em triple points}, i.e., if $i<j<k$ then there is almost surely no $t\in{\mathbb R}$ such that $X_i(t)=X_j(t)=X_k(t)$. The general setting for our model can be found in \citeN{F:2002} and \citeN{FK:2009}.

The value $X_i(t)$ of the stock $X_i$ at time $t$ represents the total capitalization of the company at that time. If we let $Z$ represent the total capitalization of the market, then
\begin{equation*}
Z(t){\triangleq} X_1(t)+\cdots+X_n(t),
\end{equation*}
and we can define the \emph{market portfolio} to be the portfolio ${\mu}$ with weight processes given by the \emph{market weights}
\begin{equation*}
{\mu}_i(t){\triangleq} \frac{X_i(t)}{Z(t)}, \quad\text{ for }i=1,\ldots,n.
\end{equation*}

We shall assume that the market
weight process ${\mu}=({\mu}_1,\ldots,{\mu}_n)$ has a stable, or \emph{steady-state,} distribution, and
that the system is in that stable distribution. We shall be interested in the relative behavior of the log-capitalizations or log-weights. If ${\mu}(t)$ is in its steady-state distribution, then the
\emph{log-difference processes} defined by
\begin{equation*}
\log X_i(t)-\log X_j(t)=\log{\mu}_i(t)-\log{\mu}_j(t),
\end{equation*}
 for $i,j=1,\ldots,n$, will also be in their steady-state distribution.

Consider the \emph{ranked capitalization processes} corresponding to the $X_i(t)$ in descending order
\begin{equation*}
X_{(1)}(t)\ge\cdots\ge X_{(n)}(t),
\end{equation*}
and the corresponding \emph{ranked market weights}
\begin{equation*}
{\mu}_{(1)}(t)\ge\cdots\ge {\mu}_{(n)}(t).
\end{equation*}
Let $r_t(i)$ represent the rank of $X_i(t)$, and let $p_t$ be the inverse
permutation of $r_t$ (with ties in rank settled by the order of the indices), so
\begin{equation*}
X_i(t)=X_{(r_t(i))}(t)\quad \text{and}\quad  X_{(k)}(t)=X_{p_t(k)}(t),
\end{equation*}
and, similarly
\begin{equation*}
{\mu}_i(t)={\mu}_{(r_t(i))}(t) \quad \text{and} \quad {\mu}_{(k)}(t)={\mu}_{p_t(k)}(t).
\end{equation*}
Hence, $p_t(k)$ represents the index, or {\em name}, of the stock occupying rank $k$ at time $t$.

The ranked market weights $({\mu}_{(1)}(t),\ldots,{\mu}_{(n)}(t))\equiv({\mu}_{p_t(1)}(t),\ldots,{\mu}_{p_t(n)}(t))$ comprise the \emph{capital distribution curve} of the market at time $t$. The capital distribution curves over several decades of the 20th century can be seen in Figure~\ref{f1}, a version of which appears in \citeN{F:2002}. The curves in Figure~\ref{f1} show the ranked market weights on December 31 of the years 1929, 1939, 1949, 1959, 1969, 1979, 1989, and 1999. During that period, the number of stocks in the market increased over each decade, so the decade associated with each curve is clear from the chart. We see that the capital distribution curve of the market shows a certain stability over time, so the assumption that ${\mu}$ is in its steady state distribution would seem to be consistent with the observed data.

\vspace{10pt}
\begin{figure}[H]
\begin{center}
\scalebox{.5}{ \rotatebox{90}{\includegraphics{Fig1-eps-converted-to.pdf}}}
\end{center}
\caption{Capital distribution of the U.S.\ market: 1929--1999.}
\centerline{The curves show the ranked weights at the end of each decade.}
\end{figure}\label{f1}

\vspace{10pt}
\noindent{\bf\large Acknowledgements.} The authors are grateful to Adrian Banner, Daniel Fernholz, Vassilios Papathanakos, and Johannes Ruf for their many helpful discussions and suggestions, as well as for their participation and inspiration during the course of this research.

\section{First-order models}

A first-order model is a stock-market model in which each stock has constant growth and variance parameters that depend only on the {\em rank} of the stock by market capitalization. These models were developed in \citeN{F:2002} and \shortciteN{BFK:2005}, and can be constructed to reflect certain properties of actual stock markets. A first-order model that is based on an actual market will have a steady-state capital distribution curve that is about the same as the capital distribution curve for the actual market (see \citeN{F:2002}, Figure 5.6).

A \emph{first-order model}  is  defined by a system ${\widehat{X}}=({\widehat{X}}_1,\ldots,{\widehat{X}}_n)$ of the form
\begin{align*}
d\log {\widehat{X}}_i(t)
&= g_{{\hat r}_t(i)}\,dt + {\sigma}_{{\hat r}_t(i)}\,dW_i(t),\\
&= {\sum_{k=1}^n} g_k\b1{{\hat r}_t(i)=k}dt
+ {\sum_{k=1}^n}{\sigma}_k\b1{{\hat r}_t(i)=k}dW_i(t),
\end{align*}
for $i=1,\ldots,n$, where $g_1,\ldots,g_n$ are real constants, ${\sigma}_1,\ldots,{\sigma}_n$ are positive constants, and $(W_1,\ldots,W_n)$ is an ${\mathbb R}^n$-valued Brownian motion, and where ${\hat r}_t(i)$ represents the rank of ${\widehat{X}}_i(t)$ (analogously to $r_t(i)$ for the rank of $X_i(t)$). We shall assume that the $g_k$ satisfy
\begin{equation*}
g_1+\cdots+g_n=0,
\end{equation*}
and
\begin{equation*}
\sum_{k=1}^m g_k<0,
\end{equation*}
for $m<n$. With these parameters, the ${\widehat{X}}_i$ form an \emph{asymptotically stable} system, which means  that the market weights ${\widehat\mu}_i(t)={\widehat{X}}_i(t)/\big({\widehat{X}}_1(t)+\cdots+{\widehat{X}}_n(t)\big)$ satisfy
\begin{equation*}
 \lim_{t\to\infty}t^{-1}\log {\widehat\mu}_i(t) = 0,\quad\text{for }i=1,\ldots,n,
\end{equation*}
and the limits corresponding to \eqref{2.2a} and \eqref{2.2z} below exist (see also \citeN{F:2002}, Definition~5.3.1).

Suppose we have a market $X$,  and suppose that its market portfolio ${\mu}$  is in the steady-state distribution.
We define the asymptotic \emph{rank-based relative variances} for the market by
 \begin{equation}\label{2.2a}
 {\bm \sigma}_k^2{\triangleq} \lim_{t\to\infty}t^{-1}\brac{\log {\mu}_{(k)}}(t),
 \end{equation}
 and the asymptotic \emph{rank-based relative growth rates}  by
 \begin{equation}\label{2.8}
  {\bm g}_k{\triangleq}{\lim_{T\to \infty}}{1}{\int^T_0} {\sum_{i=1}^n}\b1{r_t(i)=k}d\log{\mu}_i(t),
\end{equation}
 and suppose these limits exist almost surely. Since these parameters are based on the market weight processes ${\mu}_i$, they
 represent values relative to the market  portfolio ${\mu}$.

 For $k<\ell$, let ${\Lambda}{k,\ell}$ be the local time of the nonnegative semimartingale
$\log({\mu}_{(k)}/{\mu}_{(\ell)})\ge 0$ at the origin, and set ${\Lambda}{0,1} \equiv 0 \equiv {\Lambda}{n,n+1}$. Since we have assumed that the $X_i$ almost surely have no triple points, it follows that for $\ell>k+1$,  the  local time by ${\Lambda}{k,\ell}$ is identically zero, so here we need to consider only local times of the form ${\Lambda}{k,k+1}$, and we have
\begin{equation*}
d\log{\mu}_{(k)}(t)={\sum_{i=1}^n}\b1{r_t(i)=k}d\log{\mu}_i(t) +{\frac{1}{2}}\,d{\Lambda}{k,k+1}(t)-{\frac{1}{2}}\,d{\Lambda}{k-1,k}(t),{\mathrm a.s.}
\end{equation*}
For $k=1,\ldots,n-1$, we can define the \emph{asymptotic local time}
\begin{equation}\label{2.2z}
{\bm \lambda}_{k,k+1} {\triangleq}  \lim_{t\to\infty}t^{-1}{{\Lambda}{k,k+1}(t)},
\end{equation}
which exists almost surely, and define  ${\bm \lambda}_{0,1}\equiv 0\equiv{\bm \lambda}_{n,n+1}$. It turns out that the estimation of the ${\bm \lambda}_{k,k+1}$ is not difficult, and the procedure is described in the appendix of \citeN{F:2002}. It can be shown (c.f. Proposition 5.3.2 in \citeN{F:2002}) that
\begin{equation}\label{2.3}
{\bm g}_k={\frac{1}{2}}\big({\bm \lambda}_{k-1,k}-{\bm \lambda}_{k,k+1}\big),{\mathrm a.s.}
\end{equation}
holds for $k=1,\ldots,n$, and it follows that ${\bm g}_1+\cdots+{\bm g}_n=0$.

The smoothed values of ${\bm \sigma}^2_k$ and ${\bm g}_k$ for the largest 5120 stocks in the U.S. market for the decade 1990--1999 are shown in Figures~\ref{f2} and \ref{f3}. Since the number of stocks in the market changed during the decade of 1990--1999, we limit our attention here to the largest 5120 stocks, which is fewer than the number of stocks in the market at any time during that decade.
The values in Figure~\ref{f3} do not add up to zero, since the largest 5120 stocks are a strict  subset of the larger market.

The first-order model ${\widehat{X}}=({\widehat{X}}_1,\ldots,{\widehat{X}}_n)$ such that
\begin{align*}
d\log{\widehat{X}}_i(t)
&={\bm g}_{{\hat r}_t(i)}dt + {\bm \sigma}_{{\hat r}_t(i)}dW_i(t),\\
&={\sum_{k=1}^n}{\bm g}_k\b1{{\hat r}_t(i)=k}dt + {\sum_{k=1}^n}{\bm \sigma}_k\b1{{\hat r}_t(i)=k}dW_i(t),
\end{align*}
where ${\hat r}_t(i)$ is the rank of ${\widehat{X}}_i(t)$ at time $t$, is called the \emph{first-order model} for the market $X$. As we have seen, the growth and variance parameters for ${\widehat{X}}$ are derived from the relative growth and variance
parameters corresponding to the market weight processes ${\widehat\mu}_i$, not directly from the capitalization processes ${\widehat{X}}_i$.

\begin{figure}[H]
\begin{center}
\vspace*{-40pt}
\hspace*{-10pt}
\scalebox{.85}{ \rotatebox{0}{\includegraphics{Fig2-eps-converted-to.pdf}}}
\end{center}
\vspace*{-25pt}
\caption{Smoothed values of ${\bm \sigma}^2_k$, $k=1,\ldots,5120$, for U.S.\ market: 1990--1999.}\label{f2}
\end{figure}

\begin{figure}[H]
\begin{center}
\vspace*{-35pt}
\hspace*{-10pt}
\scalebox{.80}{ \rotatebox{0}{\includegraphics{Fig3-eps-converted-to.pdf}}}
\end{center}
\vspace*{-25pt}
\caption{Smoothed values of ${\bm g}_k$, $k=1,\ldots,5120$, for U.S.\ market: 1990--1999.}\label{f3}
\centerline{The ${\bm g}_k$ satisfy ${\sum_{k=1}^n}{\bm g}_k=0$, where $n{\cong} 7000$.}
\end{figure}
\vspace{10pt}

First-order models are ergodic in the sense that
\begin{equation}\label{2.20}
{\lim_{T\to \infty}}{1}{\int^T_0}\b1{{\hat r}_t(i)=k}dt={\lim_{T\to \infty}}{1}{\int^T_0}\b1{{\widehat{X}}_i(t)={\widehat{X}}_{(k)}(t)}dt=\frac{1}{n},{\mathrm a.s.}
\end{equation}
 This ergodicity property does not seem to be present in real markets, but instead there exist
\emph{asymptotic occupation rates} defined by
 \begin{equation}\label{2.2b}
\theta_{ki} {\triangleq} {\lim_{T\to \infty}}{1}{\int^T_0}\b1{r_t(i)=k}dt={\lim_{T\to \infty}}{1}{\int^T_0} \b1{X_i(t)=X_{(k)}(t)}dt,{\mathrm a.s.}
 \end{equation}
Here $\theta_{ki}$ represents the fraction of time that $X_i$ spends in the $k$th rank. The $n\times n$ matrix $\theta=(\theta_{ki})$ is bistochastic, and we shall assume that all the entries are positive. For a first-order model, \eqref{2.20} implies that $\theta_{ki}=1/n$ for all $i$ and $k$, and since this does not seem to characterize the behavior of real markets, we shall now consider a more general class of models.

\section{Second-order models}

A second-order model is a stock-market model in which each stock has constant growth and variance parameters that depend on the {\em rank} and {\em name}, or index, of the stock. Second-order models are examples of
\emph{hybrid (Atlas) models,} which were discussed in \shortciteN{IPBKF:2011}. A  {\em second-order model} is defined by a system ${\widehat{X}}=({\widehat{X}}_1,\ldots,{\widehat{X}}_n)$ of the form
\begin{align}
d\log {\widehat{X}}_i(t) &= ({\gamma}_i+g_{{\hat r}_t(i)})dt +{\sigma}_{i,{\hat r}_t(i)}\,dW_i(t)\label{3.1}\\
&= \Big({\gamma}_i+{\sum_{k=1}^n} g_k\b1{{\hat r}_t(i)=k}\Big)dt
+ {\sum_{k=1}^n}{\sigma}_{ik}\b1{{\hat r}_t(i)=k}dW_i(t),\notag
\end{align}
for $i=1,\ldots,n$, with constants $g_k$, ${\gamma}_i$ and ${\sigma}_{ik}>0$, for $i,k=1,\ldots,n$,  and a Brownian motion $W$. In order for the  ${\widehat{X}}_i$ to be asymptotically stable, these parameters must satisfy
\begin{equation*}
g_1+\cdots+g_n=0={\gamma}_1+\cdots+{\gamma}_n,
\end{equation*}
 and, for any permutation ${\pi}\in\Sigma_n$,
\begin{equation*}
\sum_{k=1}^m(g_k+{\gamma}_{{\pi}(k)})<0,\quad\text{for $m<n$.}
\end{equation*}
Here we are interested in estimating the growth-rate parameters ${\gamma}_i$ and $g_k$. For simplicity, we shall consider only rank-based variances, and assume that  ${\sigma}_{ik}^2={\sigma}^2_{k}$ for all $i$ and $k$.

It was shown in \shortciteN{IPBKF:2011} that a second-order model of the form \eqref{3.1} is asymptotically stable, and the asymptotic occupation rates
\begin{equation}\label{3.4}
{\widehat \theta}_{ki}{\triangleq} {\lim_{T\to \infty}}{1}{\int^T_0} \b1{{\hat r}_t(i)=k}\,dt
\end{equation}
are defined for all $i$ and $k$, almost surely. The matrix ${\widehat \theta}=({\widehat \theta}_{ki})$, like $\theta$ in \eqref{2.2b}, will be bistochastic with positive entries. We can generate the first-order parameters  ${\widehat{\bm \sigma}}^2_k$  and ${\widehat{\bm g}}_k$ for ${\widehat{X}}$ as in \eqref{2.2a} and \eqref{2.8}, with
 \begin{equation*}
 {\widehat{\bm \sigma}}_k^2{\triangleq} \lim_{t\to\infty}t^{-1}\brac{\log {\widehat\mu}_{(k)}}(t),
 \end{equation*}
 and
 \begin{equation*}
  {\widehat{\bm g}}_k{\triangleq}{\lim_{T\to \infty}}{1}{\int^T_0} {\sum_{i=1}^n} \b1{{\hat r}_t(i)=k}d\log{\widehat\mu}_i(t).
\end{equation*}
With these parameters, it was shown in \shortciteN{IPBKF:2011} that, almost surely,
\begin{align}
{\widehat{\bm g}}_k &= g_k + {\sum_{i=1}^n}{\widehat \theta}_{ki}{\gamma}_i\label{3.5}\\
0&= {\gamma}_i + {\sum_{k=1}^n}{\widehat \theta}_{ki}g_k.\label{3.6}
\end{align}
In matrix form, this can be expressed
\begin{align*}
{\widehat{\bm g}}&=g+{\widehat \theta}{\gamma}\\
0&={\gamma}+{\widehat \theta}^T g,
\end{align*}
where ${\gamma}$, $g$, and ${\widehat{\bm g}}$ are column vectors. From this we see that
\begin{equation}\label{4}
{\gamma}=-{\widehat \theta}^T g,
\end{equation}
so
\begin{equation}\label{1}
{\widehat{\bm g}} = \big(I_n-{\widehat \theta}\thhat^T\big)g.
\end{equation}

\section{Estimation of second-order parameters}

The  first-order growth parameters  ${\bm g}_k$  for the market $X$ can be estimated directly from  the stock return time series; however,  second-order growth parameters will have to be estimated indirectly. We wish to construct a second-order model that has first-order growth parameters equal to those of the market, and an occupation-rate matrix equal to the occupation-rate matrix $\theta$ of the market. Under these circumstances, as in  \eqref{1}, we have
\begin{equation}\label{4.1a}
{\bm g} = \big(I_n-\theta\theta^T\big)g,
\end{equation}
and we wish to solve this equation for  $g$, the vector of name-based growth parameters for the  second-order model of  the market $X$. If we can solve \eqref{4.1a} for this $g$, then we can use \eqref{4}, in the form
\begin{equation}\label{4.1b}
{\gamma}=-\theta^T g,
\end{equation}
to generate the name-based growth parameters ${\gamma}_i$ for this second-order model. Let us first consider the matrix $\theta$.

The matrix $\theta$ is bistochastic and we have assumed that all its entries are positive, so this also holds for $\theta^T$ and $\theta\theta^T$. By the Perron-Frobenius theorem (see \citeN{Perron:1907}), the symmetric matrix $\theta\theta^T$ will have a simple eigenvalue equal to 1 with eigenvector $e_1=(1,1,\ldots,1)'$, and all the other eigenvalues will have absolute value less than 1. Hence, $I_n-\theta\theta^T$ has rank $n-1$ and its kernel is generated by $e_1$, so the condition that the $g_k$ sum to zero means that $g$ is orthogonal to this kernel, and this ensures a unique solution to \eqref{4.1a}.

Unfortunately,  it seems to be essentially impossible to estimate $\theta$ with any reasonable accuracy, so although we can use this matrix to prove the existence and uniqueness of $g$, in practice we cannot actually solve equation \eqref{4.1a}.
Instead, let us consider \eqref{3.5} in the form
\begin{equation}\label{4.3a}
{\bm g}_k = g_k + {\sum_{i=1}^n}\theta_{ki}{\gamma}_i.
\end{equation}
We can use this equation to generate the $g_k$ recursively, and then estimate the ${\gamma}_i$  from the returns data and the $g_k$.

Let  us assume that the market $X$ is defined for all $t\in{\mathbb R}$, that the weight process ${\mu}$ for $X$ has a stable distribution, and that ${\mu}$ is in that stable distribution. We can then define the \emph{time-reversed} market ${\widetilde{X}}$ with stock capitalizations ${\widetilde{X}}_i(t){\triangleq} X_i(-t)$ and weights ${\widetilde\mu}_i(t){\triangleq} {\mu}_i(-t)$, and with this definition we can define the expected backward occupation rates similarly to \eqref{2.2b}. Since the weight process is in its steady-state distribution, the limits of \eqref{2.2b} will be the same at plus and minus infinity, so the forward and backward expected occupation rates $\theta_{ki}$ will be equal.  The results of \citeN{Bertoin:1987} imply that the forward and backward asymptotic local times ${\Lambda}{k,k+1}$ will also be the same, so the forward and backward versions of the ${\bm \lambda}_k$ are equal. Hence, it follows from \eqref{2.3} that the forward and backward ${\bm g}_k$ are equal. In this case, \eqref{4.1a} implies that the forward and backward values of the $g_k$ are equal, and from  \eqref{4.1b}, we see that the forward and backward ${\gamma}_i$ are also equal. Quadratic variation is invariant under time reversal, so the forward and backward ${\bm \sigma}_k$ will be the same. Hence, the  first- and second-order models for $X$ are the same as the corresponding models for ${\widetilde{X}}$, and this allows us to use both $X$ and ${\widetilde{X}}$ to estimate the second-order parameters.

In order to estimate the second-order parameters, it is necessary to observe the movement of market weights forward and backward in time. To this end, we define the concept of \emph{flow} in a market.
The \emph{forward flow}  ${\phi}_k$ of the market at rank $k$  is defined for ${\tau}\ge0$ by
\begin{equation*}
{\phi}_k({\tau}){\triangleq}{\lim_{T\to \infty}}{1}{\int^T_0}\log\Big(\frac{{\mu}_{p_t(k)}(t+{\tau})}{{\mu}_{(k)}(t)}\Big)dt,
\end{equation*}
and the \emph{backward flow}  $\widetilde{{\phi}}_k$ of the market is defined by
\begin{equation*}
\widetilde{{\phi}}_k({\tau}){\triangleq}{\lim_{T\to \infty}}{1}{\int^T_0}\log\Big(\frac{\widetilde{\mu}_{p_t(k)}(t+{\tau})}{\widetilde{\mu}_{(k)}(t)}\Big)dt.
\end{equation*}
In Figure~\ref{f4} we see the exponential of forward and backward flow for the largest 250 stocks in the U.S. market over the decade from 1990 to 1999. The plots  show the average exponential flow of each of the ten deciles of the top 250 stocks, with each decile comprising 25 stocks. The forward and backward flows need not be equal, and they do not appear to be equal in Figure~\ref{f4}. We see from the chart that for the largest 250 stocks the flow is downward. For the smaller stocks, we would expect the flow to be upward.

If we follow the flow of a stock that occupies a given rank at time zero, then the expected rank of the stock will change over time according to its flow.
Suppose a stock is at rank $k$ at time 0, and
let us estimate  its  expected rank at time ${\tau}\in{\mathbb R}$ by
\begin{equation*}
{\bf R}_k({\tau}){\triangleq} {\lim_{T\to \infty}}{1}{\int^T_0} r_{s+{\tau}}(p_s(k))\,ds.
\end{equation*}
In this case, ${\bf R}_k(0)=k$, and if this rank is among the higher ranks, we would expect the flow to be negative, which would mean that for ${\tau}>0$ we would expect that ${\bf R}_k({\tau})\le k$ and ${\bf R}_k(-{\tau})\le k$. We would like to use the ${\bf R}_k$ to estimate the $g_k$, and although ${\bf R}_k({\tau})$ need not equal ${\bf R}_k(-{\tau})$, the $g_k$ generated using either one will provide estimates for the solution of \eqref{1}. Accordingly, we shall  use the average of the two, with
\begin{equation*}
{\overline\RR}_k({\tau}){\triangleq}\Bigg[\frac{{\bf R}_k({\tau})+{\bf R}_k(-{\tau})}{2}\Bigg],
\end{equation*}
where the brackets signify the nearest integer. Values of ${\bf R}_k({\tau})$ for $k=1,\ldots,250$ and ${\tau}=\pm4$ are shown in Figure~\ref{f5}, and the values for positive and negative ${\tau}$ are clearly different. We have no explanation for this difference.

Figure~\ref{f4} was generated by following the market weights of stocks that occupied a given rank at a given time in the decade from January 1, 1990 to December 31, 1999. Since stocks enter and leave the market, we used only the largest 250 stocks, after eliminating any stocks that did not have a full ten-year history. The trajectories of the weights for each to the top 250 ranks were followed for 1000 days forward or backward, and were then averaged over all starting dates that would allow the full 1000 days to be used. Finally, the ranks were separated into deciles, with ranks 1--25 in the first decile, 26--50 in the second decile, and so forth. The curves in Figure~\ref{f4} represent the average trajectories for the weights of each of the ten deciles, forward and backward.

Figure~\ref{f5} was generated by following the weight trajectories used for Figure~\ref{f4} and, for each trajectory, noting the starting rank and ending rank, i.e., the rank after 1000 days (approximately four years of trading days). The final rank corresponding to the initial rank $k$ in Figure~\ref{f5} is the average ending rank for those trajectories that begin at rank $k$ at time 0. This was carried out in forward time and reversed time.

\begin{figure}[H]
\begin{center}
\vspace*{-15pt}
\hspace*{-20pt}
\scalebox{.58}{ \rotatebox{90}{\includegraphics{Fig4-eps-converted-to.pdf}}}
\end{center}
\vspace*{-20pt}
\caption{${\mu}_{(k)}(0)e^{{\phi}_k({\tau})}$ (black, solid),  ${\mu}_{(k)}(0)e^{\widetilde{{\phi}}_k({\tau})}$ (red, dotted): 1990--1999. On average,}\label{f4}
\centerline{ a stock that starts at time 0 at rank $k$ with market weight ${\mu}_{(k)}(0)$ will move to weight }
\centerline{${\mu}_{(k)}(0)e^{{\phi}_k({\tau})}$ at time ${\tau}\in[0,1000]$, or to weight ${\mu}_{(k)}(0)e^{\widetilde{\phi}_k({\tau})}$ in reversed time. }
\end{figure}

\begin{figure}[H]
\begin{center}
\vspace*{-5pt}
\hspace*{-20pt}
\scalebox{.725}{ \rotatebox{0}{\includegraphics{Fig5-eps-converted-to.pdf}}}
\end{center}
\vspace*{-20pt}
\caption{${\bf R}_k(4)$ (black, solid) and ${\bf R}_k(-4)$ (red, dotted): 1990--1999.} \label{f5}
\centerline{On average, a stock that starts a given initial rank will move  to the }
\centerline{corresponding final rank four years later, or earlier, in reversed time.}
\centerline{The straight line represents final rank $=$ initial rank.}
\end{figure}
\vspace{10pt}

Let ${\bf G}_k({\tau})$ be the expected  growth rate at time ${\tau}\in{\mathbb R}$ of a stock which
occupies rank $k$ at time 0, and we shall estimate ${\bf G}_k({\tau})$ and  ${\bf G}_k(-{\tau})$  from the slope of the forward and backward flow at rank $k$, so
\begin{equation}\label{4.4}
{\bf G}_k({\tau})=D_{\tau} {\phi}_k({\tau})\quad\text{and}\quad{\bf G}_k(-{\tau})=D_{\tau} \widetilde{{\phi}}_k({\tau}),
\end{equation}
for ${\tau}\ge 0$, with ${\bf G}_k(0) ={\bm g}_k$.
We shall use the average
\begin{equation*}
{\overline\GG}_k({\tau}){\triangleq}{\frac{1}{2}}\big({\bf G}_k({\tau}) +{\bf G}_k(-{\tau})\big)
\end{equation*}
 to estimate the rank-based growth rates $g_k$. In the data we analyzed, the derivatives in \eqref{4.4} at ${\tau}=4$ were estimated by measuring the rate of change of the flows ${\phi}({\tau})$ and $\widetilde{\phi}({\tau})$ for the period from day 981 to day 1000, and then annualizing this rate.

Since for a given stock the name-based growth rate is invariant with rank, the same holds for the  average of the name-based growth rates weighted by occupation rates,
\begin{equation*}
{\sum_{i=1}^n}{\widehat \theta}_{ki}{\gamma}_i.
\end{equation*}
Hence,
\begin{equation}\label{4.1}
{\overline\GG}_k({\tau}){\cong}  g_{{\overline\RR}_k({\tau})}+{\sum_{i=1}^n}{\widehat \theta}_{ki}{\gamma}_i,
\end{equation}
for ${\tau}\in{\mathbb R}$, where
\begin{equation*}
g_{{\overline\RR}_k({\tau})}{\triangleq}\big(\ell+1-{\overline\RR}_k({\tau})\big)\,g_\ell+\big({\overline\RR}_k({\tau})-
\ell\big)\,g_{\ell+1},
\end{equation*}
and $\ell$  the largest integer such that $\ell\le{\overline\RR}_k({\tau})$. If we combine \eqref{4.1} with \eqref{3.5}, we find that
\begin{equation}\label{4.2}
g_{{\overline\RR}_k({\tau})} {\cong} g_k+{\overline\GG}_k({\tau}) -{\bm g}_k.
\end{equation}
 We can first estimate ${\bm g}_k$, ${\overline\GG}_k({\tau})$, and ${\overline\RR}_k({\tau})$, and then use \eqref{4.2} to recursively generate the values of the rank-based growth rates $g_k$ for a subsequence of ranks of the form $k,{\overline\RR}_k({\tau}),{\overline\RR}_{{\overline\RR}_k({\tau})}({\tau}),\ldots$, as well as interpolated points.

Once we have estimates for the  values of  the $g_k$,  we can estimate the ${\gamma}_i$ directly by using
\begin{equation}\label{4.3}
{\gamma}_i={\frac{1}{2}}\Big({\lim_{T\to \infty}}{1}{\int^T_0}\big(d\log {\mu}_i(t) - g_{r_t(i)}\,dt\big)+
{\lim_{T\to \infty}}{1}{\int^T_0}\big(d\log {\widetilde\mu}_i(t) - g_{r_t(i)}\,dt\big)\Big).
\end{equation}
Our second-order model for the market $X$ will then be
\begin{equation*}
d\log {\widehat{X}}_i(t) = ({\gamma}_i+g_{{\hat r}_t(i)})dt +{\sigma}_{{\hat r}_t(i)}\,dW_i(t).
\end{equation*}

The various steps in the estimation process are shown in Figures~\ref{f6}, \ref{f7}, and \ref{f8}. In Figure~\ref{f6} we see the estimated forward rank ${\overline\RR}_k(4)$ versus the initial rank $k$, and find that the relation is quite close to linear with
\begin{equation*}
{\overline\RR}_k(4) {\cong} 4.6 + 1.16k.
\end{equation*}
With this estimate, we can use \eqref{4.2} in the form
\begin{equation}\label{4.4}
g_{(4.6 + 1.16k)} {\cong} g_k+{\overline\GG}_k(4) -{\bm g}_k
\end{equation}
to estimate the $g_k$ from the values of ${\bm g}_k$ and ${\overline\GG}_k(4)$.

The values of ${\overline\GG}_k$ were estimated from the slopes of the flows used to generate Figure~\ref{f4} for the ten rank-decile groups of 25 stocks each from the largest 250 stocks. Linear approximations for all the ranks were generated using a least squares fit. These results appear in Figure~\ref{f7}, and the corresponding linear equations are
\begin{equation*}
{\overline\GG}_k(0)=-4.2-.034k\quad\text{ and }\quad{\overline\GG}_k(4)=-4.5-.027k.
\end{equation*}
By using the values derived from these equations in \eqref{4.4} we can generate values for $g_k$ for an increasing sequence of ranks $k$. The chart in Figure~\ref{f8} shows these values with linear interpolation connecting the points to generate a continuous curve.

\bigskip

\begin{figure}[H]
\begin{center}
\hspace*{-20pt}
\scalebox{.58}{ \rotatebox{90}{\includegraphics{Fig6-eps-converted-to.pdf}}}\end{center}
\caption{Estimated four-year forward rank ${\overline\RR}_k(4)$ corresponding to initial rank $k$.}\label{f6}
\centerline{${\overline\RR}_k(4){\cong} 4.6+1.16k$.}
\end{figure}

\begin{figure}[H]
\begin{center}
\hspace*{-20pt}
\scalebox{.58}{ \rotatebox{0}{\includegraphics{Fig7-eps-converted-to.pdf}}}
\end{center}
\vspace*{-15pt}
\caption{Estimated expected growth rates ${\overline\GG}_k(0)$ and ${\overline\GG}_k(4)$ at rank $k$.} \label{f7}
\centerline{${\overline\GG}_k(0){\cong}-4.2-.034k$ (black, solid line; dots),}
\centerline{${\overline\GG}_k(4){\cong}-4.5-.027k$ (red, broken line; circles).}
\end{figure}

\begin{figure}[H]
\begin{center}
\hspace*{-20pt}
\scalebox{.58}{ \rotatebox{0}{\includegraphics{Fig8-eps-converted-to.pdf}}}\end{center}
\vspace*{-15pt}
\caption{Values of $g_k$ for ranks 1 to 250, calculated recursively and interpolated from } \label{f8}
\centerline{ $g_{(4.6 + 1.16k)} {\cong} g_k+{\overline\GG}_k(4) -{\bm g}_k$. The $g_k$ here are not normalized to add up to 0.}
\end{figure}

Once we have estimates for the values of the $g_k$, we can use these values along with \eqref{4.3} to estimate values for the ${\gamma}_i$ of individual stocks by name. The integrals in \eqref{4.3} were approximated by daily logarithmic relative returns taken for each of the stocks along with the values of the $g_k$. The (non-normalized) values for ${\gamma}_i$ for the decade 1990--1999 for a number of well-known stocks appear in Table~\ref{t1}. This is hardly a definitive study, so only a few stocks are included here. Moreover, in some future work, it would be desirable to have confidence intervals for these values, rather than point estimates. In that regard, probably the most promising method would use some form of jackknife estimator, with perhaps 12 pseudovalues generated by leaving out one month of the year at a time (see \citeN{Mosteller/Tukey:1977}). Probably the entire estimation process would need to be repeated for each pseudovalue.

The values in Table~\ref{t1} were estimated using combined forward and backward estimates, as in \eqref{4.3}, for the decade  1990--1999. Using only forward estimates or only backward estimates for the ${\gamma}_i$ could have produced biased estimates, since some of these companies grew considerably over that decade. For each company, the number in parentheses is the rank of the time-averaged log-weight of the stock during the decade.

While the values in Table~\ref{t1} may not be definitive, they at least appear plausible. The higher-ranked stocks have generally higher ${\gamma}$, which should help them maintain their positions at the top of the market. At this writing, Apple, AAPL,  has the highest market capitalization in the U.S. market, but in the 1990s we see that its average rank was 93, and its ${\gamma}$ is correspondingly $-1.67\%$. Hence, the estimated ${\gamma}_i$ provide no miraculous forecasts of future behavior; instead they reflect local stability consistent with the observed decade.

\begin{table}[H]
\caption{Values of ${\gamma}_i$ for various companies, 1990--1999.}\label{t1}
\begin{center}
\begin{tabular}{l>{$}r<{$}}
 Apple, AAPL (93) & -1.67\%  \\
 Coca Cola, KO (4)  & 0.26\%\\
Exxon, XON (3)  &0.11\% \\
  General Electric, GE (1) &0.14\%\\
International Business Machines, IBM (6) &\quad -0.10\%  \\
 Microsoft, MSFT (5)  & -0.12\%
\end{tabular}
\end{center}
\label{default}
\end{table}

\section{Conclusion}

The purpose of first- and second-order models for stock markets is to create a rigorous backdrop for the statistical analysis of the behavior of individual stocks. Second-order models provide a more accurate and complete representation of a stock market than is possible in first-order models. The estimation of parameters for second-order models is more involved than for first-order models, and implicit methods must be used. We have proposed methods for the estimation of second-order growth rate parameters, and with these methods a more complete stock-market model is possible. Nevertheless, our techniques are rudimentary, and we believe that future research will yield significant improvements.

\bibliographystyle{plainnat}

redpajama_set_name: RedPajamaArXiv


What are Optics and Photonics?
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I'm Katie Francis. You can find me persuading friends to pack their travel bags, day-dreaming about my next adventure, or Googling cheap flights. Adventuring is my passion.
I've always wanted to share my stories and I finally got the balls to start a blog. This blog is intended for anyone who wants to experience the world, laugh at my travel wanderings, learn more about international travel, and get tips and ideas for your next adventure.
Anytime I go on a trip I think of myself as Indiana Jones (theme song included). What I love about Indy is that he isn't a superhero. He falls down, gets hurt, and gets back up. You don't need superpowers to travel the world. I surely don't have any. In one of the movies, I don't remember which one, Indy states: "If you want to be a good archaeologist, you gotta get out of the library." Same goes for travelling. If you want to really experience another culture, you have to get out of your comfort zone. This is what I aim to do. Follow me in my Silly Bits section and giggle at my tales from my past. Take notes from my Travel Tips section, where I share my recommendations and itineraries.
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Where did your love of travel come from? My love began in France, a place where every girl dreams of falling in love, a place that has romance written all over it. Maybe the first city that comes to your mind is Paris, the "City of Love", but my journey started about three hours south of Paris in the spa town of Vichy. My junior year of undergrad I said "See ya Missouri, Bonjour France!" In Vichy I studied International Business and French at University Blaise-Pascal. Originally, I signed up for a semester, but I had such a great time I decided to stay for two. During those ten months I travelled throughout Europe and this where the itch started. I've been scratching it ever since.
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